LTI system and closed loop in modern systems

Linear time-invariant (LTI) system

A system is linear if it obeys the principle of superposition (additivity and homogeneity): if $r_1 \to c_1$ and $r_2 \to c_2$, then $a r_1 + b r_2 \to a c_1 + b c_2$. It is time-invariant if its parameters do not change with time, so a delayed input gives an equally delayed output: $r(t-T) \to c(t-T)$.

An LTI system is described by a linear differential equation with constant coefficients, e.g.

$$a_2\ddot c + a_1\dot c + a_0c = b_0r$$

and can be represented by a transfer function $G(s) = C(s)/R(s)$. Example: an RLC circuit with fixed R, L, C.

"Modern complex systems are more pronounced with closed-loop control"

Modern systems (power grids, aircraft, robots, process plants) have many interacting parts, changing loads and strict accuracy needs. Closed-loop control suits them because:

1. Low sensitivity: $S_G^T = \dfrac{1}{1+GH}$, so ageing and parameter changes hardly affect the output.
2. Disturbance rejection: load and noise effects are cut by $(1+GH)$.
3. Faster response: time constant $\tau/(1+K)$.
4. Stabilization: inherently unstable systems (fighter aircraft, maglev, rockets) can be operated.
5. Automation: cheap sensors and digital controllers make feedback easy and allow operation without humans.

So the statement is justified; open loop is used only where the system is simple and well known (washing-machine timer, traffic timer).